QZ 4-B - f ( x , y ) = 6 y x + , 0 < x...

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STAT 400 Fall 2011 Version B Name ANSWERS . Quiz 4 (10 points) Be sure to show all your work; your partial credit might depend on it. If the answer is a function, its support must be included. No credit will be given without supporting work. 1. Let the joint probability density function for ( X , Y ) be f ( x , y ) = 6 y x + , 0 < x < 1, 0 < y < 3, zero otherwise. a) (4) Find the probability P ( X < Y ). P ( X < Y ) = ∫ ∫ + - 1 0 0 6 1 dx dy y x x = + - 1 0 2 2 12 6 1 dx x x = - 1 0 2 4 1 dx x = 12 1 1 - = 12 11 . OR P ( X < Y ) = ∫ ∫ + 1 0 3 6 dx dy y x x = OR P ( X < Y ) = ∫ ∫ + 1 0 0 6 dy dx y x y + ∫ ∫ + 3 1 1 0 6 dy dx y x =
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Unformatted text preview: f ( x , y ) = 6 y x + , 0 &lt; x &lt; 1, 0 &lt; y &lt; 3, zero otherwise. b) (3) Find the marginal probability density function of X, f X ( x ). f X ( x ) = + 3 6 dy y x = 3 12 6 2 + y y x = 4 3 2 + x , 0 &lt; x &lt; 1. c) (3) Are X and Y independent? Justify your answer. No credit will be given without proper justification. Circle one: Yes. No. f Y ( y ) = + 1 6 dx y x = 1 6 12 2 + y x x = 12 2 1 y + , 0 &lt; y &lt; 3. f ( x , y ) f X ( x ) f Y ( y ). X and Y are NOT independent ....
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QZ 4-B - f ( x , y ) = 6 y x + , 0 &amp;amp;lt; x...

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